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I have a complex question.

Is there any other way to model the preference misalignments of the sendres (in senders-receivers games) towards the desire of some specific state apart from the quadratic loss functions? Why not quadratic gains functions? I understand that it is a bit intuitive to use this model, but is there any other model that is also used for such situations?

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Quadratic loss is convenient because it provides a close form solution after investigating the first order conditions.

That said, if you're interested in belief updating, an absolute loss function can modify (slow down) the update when a signal happens to be a the tail of the distribution and look like an outlier.

You might also consider a composite function $L$ (for example a weighted average of a quadratic loss and absolute loss) to control how fast those updates are made. Let $x^*$ be the true value, and $x$ an estimate $$L_{x^*}(x)=\alpha \left( x^* - x \right)^2 + \beta \left| x^* - x \right| $$ where $\alpha$ and $\beta$ could be any non-negative real number (e.g. $\alpha=\beta=0.5$).

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  • $\begingroup$ A weighted average of a quadratic loss and absolute loss? How would it look like? Could you write down the formula that you have in mind? $\endgroup$ Dec 31, 2023 at 10:37
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    $\begingroup$ It's done, please let me know if you have further questions. $\endgroup$ Dec 31, 2023 at 22:56
  • $\begingroup$ Thank you! I will check this out! $\endgroup$ Dec 31, 2023 at 22:57

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